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Magazine Problem 22
Compute the left and right Riemann sums \(-L_{4}\) and \(R_{4},\) respectively-for \(f(x)=\sqrt{4-x^{2}}\) on [-2,2] and compare their values.
Problem 23
Compute the left and right Riemann sums \(-L_{6}\) and \(R_{6},\) respectively - for \(f(x)=\sqrt{9-(x-3)^{2}}\) on [0,6] and their values.
Problem 24
Express the following endpoint sums in sigma notation but do not evaluate them. $$ L_{30} \text { for } f(x)=x^{2} \text { on }[1,2] $$
Problem 26
Express the following endpoint sums in sigma notation but do not evaluate them. $$ R_{20} \text { for } f(x)=\sin x \text { on }[0, \pi] $$
Problem 27
Express the following endpoint sums in sigma notation but do not evaluate them. $$ R_{100} \text { for } \ln x \text { on }[1, e] $$
Problem 28
In the following exercises, graph the function then use a calculator or a computer program to evaluate the following left and right endpoint sums. Is the area under the curve between the left and right endpoint sums? [T] \(L_{100}\) and \(R_{100}\) for \(y=x^{2}-3 x+1\) on the interval [-1,1]
Problem 29
In the following exercises, graph the function then use a calculator or a computer program to evaluate the following left and right endpoint sums. Is the area under the curve between the left and right endpoint sums? $$ \text { [T] } L_{100} \text { and } R_{100} \text { for } y=x^{2} \text { on the interval }[0,1] $$
Problem 30
In the following exercises, graph the function then use a calculator or a computer program to evaluate the following left and right endpoint sums. Is the area under the curve between the left and right endpoint sums? $$ \text { [T] } L_{50} \text { and } R_{50} \text { for } y=\frac{x+1}{x^{2}-1} \text { on the interval }[2,4] $$
Problem 31
In the following exercises, graph the function then use a calculator or a computer program to evaluate the following left and right endpoint sums. Is the area under the curve between the left and right endpoint sums? $$ \text { [T] } L_{100} \text { and } R_{100} \text { for } y=x^{3} \text { on the interval }[-1,1] $$
Problem 32
In the following exercises, graph the function then use a calculator or a computer program to evaluate the following left and right endpoint sums. Is the area under the curve between the left and right endpoint sums? $$ \text { [T] } L_{50} \text { and } R_{50} \text { for } y=\tan (x) \text { on the interval }\left[0, \frac{\pi}{4}\right] $$
